Short, Ian
(2008).
Reversible maps in isometry groups of spherical, Euclidean and hyperbolic space.
Mathematical Proceedings of the Royal Irish Academy, 108A(1),
pp. 33–46.
(
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Abstract
An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps and those maps that are expressible as a composite of three involutions are determined in the isometry groups of spherical, Euclidean and hyperbolic space in several dimensions.
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